In quantitative positron emission tomography (PET) imaging, the attenuation background of the tissue is necessary to reconstruct a radioactive tracer distribution. A PET image reconstructed with an incorrect attenuation map or without this information would suffer from significant attenuation artifacts. Methods for estimating an attenuation map can be generally categorized into two main classes, transmission and non-transmission.
Transmission methods are based on transmission data acquisition with an external radionuclide source, computed tomography (CT), or magnetic resonance imaging (MRI) scan. In a PET/CT system, attenuation correction can be achieved with the CT component. However, there are significant mismatches between not only CT and PET attenuation backgrounds but also their geometrical accuracies, which can cause substantial artifacts. When a correlation between CT and PET linear attenuation coefficients is established, low dose CT for attenuation correction has been used (Xia et al., “Limits of ultra-low dose CT attenuation correction for PET/CT,” Nuclear Science Symposium Conference Record (NSS/MIC), 2009 IEEE; Xia et al., “Ultra-low dose CT attenuation correction for PET/CT,” Physics in Medicine and Biology, 2012, 57(2):309). To compensate for the respiratory motion, a long CT acquisition time can be used.
Non-transmission methods derive the attenuation map without a separate transmission scan. In the case of brain or abdominal imaging, in which soft tissue is the dominant constituent, a uniform attenuation coefficient is assigned within a contour, which can be obtained manually or automatically. Other non-transmission methods estimate the attenuation map from the emission data alone. Welch et al. used the consistency condition of the Radon transform to estimate regions of fairly uniform attenuation (Welch et al., “Attenuation correction in PET using consistency information,” IEEE Transactions on Nuclear Science, 1998, 45(6):3134-3141). Bronnikov utilized a discrete consistency condition for the same purpose (Bronnikov, “Reconstruction of attenuation map using discrete consistency conditions,” IEEE Transactions on Medical Imaging, 2000, 19(5):451-462). In addition, techniques that attempt to reconstruct the activity and the attenuation simultaneously based on a statistical model have suffered from cross-talk artifacts.